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A096375 Number of partitions of n such that the least part occurs with odd multiplicity. 3
1, 1, 3, 2, 6, 6, 11, 11, 22, 23, 37, 42, 65, 76, 111, 127, 182, 217, 294, 351, 471, 562, 734, 881, 1137, 1364, 1733, 2074, 2608, 3127, 3883, 4644, 5732, 6838, 8367, 9963, 12113, 14395, 17396, 20614, 24785, 29314, 35059, 41360, 49270, 57979, 68775, 80753 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: Sum_{m>=1} ((x^m/(1+x^m))/Product_{i>=m}(1-x^i)).

A096374(n) + a(n) = A000041(n).

MAPLE

b:= proc(n, i) option remember; `if`(i<1, 0, `if`(irem(n, i, 'r')=0

      and irem(r, 2)=1, 1, 0)+ add(b(n-i*j, i-1), j=0..n/i))

    end:

a:= n-> b(n, n):

seq(a(n), n=1..50);  # Alois P. Heinz, Feb 27 2013

MATHEMATICA

f[n_] := Block[{p = IntegerPartitions[n], l = PartitionsP[n], c = 0, k = 1}, While[k < l + 1, If[ OddQ[ Count[ p[[k]], p[[k]][[ -1]] ]], c++ ]; k++ ]; c]; Table[ f[n], {n, 50}] (* Robert G. Wilson v, Jul 23 2004 *)

b[n_, i_] := b[n, i] = If[i<1, 0, {q, r} = QuotientRemainder[n, i]; If[r == 0 && Mod[q, 2] == 1, 1, 0] + Sum[b[n - i*j, i-1], {j, 0, n/i}]] ; a[n_] := b[n, n]; Table[a[n], {n, 1, 50}] (* Jean-Fran├žois Alcover, Jan 24 2014, after Alois P. Heinz *)

PROG

(PARI) {q=sum(m=1, 100, (x^m/(1+x^m))/prod(i=m, 100, 1-x^i, 1+O(x^60)), 1+O(x^60)); for(n=1, 47, print1(polcoeff(q, n), ", "))} - Klaus Brockhaus, Jul 21 2004

CROSSREFS

Cf. A000041, A096374.

Sequence in context: A023360 A154028 A157793 * A062200 A114208 A014686

Adjacent sequences:  A096372 A096373 A096374 * A096376 A096377 A096378

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jul 19 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v and Klaus Brockhaus, Jul 23 2004

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)